An iterative substructuring method for the hp-version
of the BEM on quasi-uniform triangular meshes
Norbert Heuer, Florian Leydecker, Ernst P. Stephan
Numer. Methods Partial Differential Eq. 23 (4), 879-903, 2007.
We study an additive Schwarz based preconditioner for the hp-version of
the boundary element method with quasi-uniform triangular meshes and for hypersingular
integral operators. The model problem is Laplace's equation exterior to an
open surface and is generic for elliptic boundary value problems of second
order in bounded and unbounded domains with closed or open boundary.
The preconditioner is based on a non-overlapping subspace decomposition into
a so-called wire basket space and interior functions for each element.
We prove that the condition number of the preconditioned stiffness matrix
has a bound which is independent of the mesh size h and which grows only
polylogarithmically in p, the maximum polynomial degree.
Numerical experiments confirm this result.